When it comes to conventional shelf systems and sliding-shelf systems, the product separators or compartment dividers are not adequately secured on the sides and they buckle if the products exert too much pressure. Sometimes, the compartment dividers consist of individual elements which have been inserted next to one another but which are not firmly attached to each other so that the product rack becomes unstable (DE 196 09 432). The shelves or shelf racks known so far have inserts with open slotted rails into which the compartment dividers in the form of brackets are inserted (U.S. Pat. No. 6,116,436). In the case of these systems as well, the compartment dividers do not provide adequate lateral support for the products. Low products roll or slide sideways underneath the brackets. If the brackets, as compartment dividers, were to be inserted only into the open slotted rails, they would not be sufficiently supported, so that for this system (U.S. Pat. No. 6,116,436), additional features that are laborious to produce, like holes into which the brackets can be inserted, have to be created so that the brackets can also be affixed horizontally. In the prior-art systems, the insertion of the brackets is complicated since they usually have to be pressed together using both hands in order to fit through the slots and, at the same time, to be inserted into the holes (U.S. Pat. No. 6,116,436). EP 1455620 solves this problem. EP 1455620 ensures a variable system with racks of shelves and especially sliding shelves according to the “first-in-first-out” method. In this manner, every conceivable type of product can be displayed while always ensuring that the products can slide. Furthermore, EP 1455620 ensures stability over the entire width of the shelf rack, thus preventing any slipping of the product dividers or of the stored products. The product separators ensure that the products reliably slide down in the compartment and also prevent sideways tipping, even when the adjacent compartment is empty. The compartment dividers or product separators in this system can be easily inserted with just one hand. The configuration consisting of several components and the special design of the rack frame as well as of the separating bracket calls for special measures of a technical nature that cannot be found in the existing systems. In particular, the system from EP 1455620 cannot be inserted into existing shelf racks since the fastening means for the product separator extends into the shelf base. Installing such a frame for the shelf rack, including the product slide plate into which the product separator is inserted, is not practicable since too much height is added to the product slide rails when such a system is installed. Furthermore, if EP 1455620 were configured as a retrofitting system, it would be technically extremely elaborate as well as costly to manufacture since it would have to be specially adapted and fit into the existing systems.